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RUDIMENTS

OF

A RITHMETIC;

CONTAINING

NUMEROUS EXERCISES

FOR THE

S). ATE AND BLAOKBOARD,

FOR BEGINNERS

BY JAMES B. THOMSON, A.M.,
AUTHOR OF MENTAL ARITHMETIC; EXERCISES IN ARITHMETICAL ANALYSI*
PRACTICAL ARITHMETIC; WTG HER ARITHMETIC; EDITOR OF DAY 8

SCHOOL ALGEBRA; LEGENDRE'S GEOMETRY, ETC.

NEW YORK:
IVISON & PHINNEY, 48 & 50 WALKER ST.

CHICAGO: S. C. GRIGGS & CO., 39 & 41 LAKE ST.
OLNOINNATI: MOORE, WILSTACH, KEYS & 00. ST. LOUIS: KEITI & WOODA.
PHILADELPHIA ; SOWER, BARNES & 00. BUFFALO: PHINNEY 00.

NEWBURG : T. 8. QUACKENBUBI,

18 5 9.

Entered according to Act of Congress, in the year 1879, bny

JAMES B. THOMSON,

la the Clerk's Office for the Southern District or Now Yact

67304

ITEREOTYPED BY TUOMAS B. OYITL.

216 WILLIAK BTREET, N. Y.

PREFACE.

EDUCATION, in its comprehensive sense, is the business of life. The exercises of the school-room lay the foundation; the superstructure is the work of after years. If these exercises are rightly conducted, the pupil obtains the rudiments of science, and what is more important, he learns how to study, how to think and reason, and is thus enabled to appropriate the means of knowledge to his future advancement. Any system of instruction, therefore, which does not embrace these objects, which treats a child as a mere passive recipient, is palpably defective. It is destitute of some of the most essential means of mental development, and is calculated to produce pigmies, instead of giant intellects.

The question is often asked, “What is the best method of proceeding with pupils commencing the study of Arithmetic, or entering upon a new rule ?"

The old method. Some teachers allow every pupil to cipher on his own hook;" to go as fast, or as slow as he pleases, without reciting a single example or rule, or stopping to inquire the “why and the wherefore” of a single operation. This mode of teaching is a relic of by-gone days, and is prima Jacie evidence, that those who practice it, are behind the spirit of the times.

Another method.-Others who admit the necessity of teaching arithmetic in classes, send their pupils to their seats, and tell them to “study the rule.” After idling away an hour or more, up goes one little hand after another with the despairing question:-“ Please to show me how to do this sun, sir ?" The teacher replies, “Study the rule ;—that will tell you.” At length, to silence their increasing importunity, he takes the slate, solves the question, and, without a word of

explanation, returns it to its owner. He thus goes through the class. When the hour of recitation comes, the class is not prepared with the lesson. They are sent to their seats to make another trial, which results in no better success. And what is the consequence? They are discouraged and disgusted with the study.

A more excellent woy.Other teachers pursue a more excellent way, especially for young pupils. It is this :—The teacher reads over with the class the preliminary explanations, and after satisfying himself that they understand the meaning of the terms, he calls upon one to read and analyze the first example, and set it down upon the blackboard, while the rest write it upon their slates. The one at the board then performs the operation audibly, and those with their slates follow step by step.

Another is now called to the board and requested to set down the second example, while the rest write the same apon their slates, and solve it in a similar manner. He then directs them to take the third example, and lets them try their own skill, giving each such aid as he may require. In this way they soon get hold of the principle, and if now sent to their seats, will master the lesson with positive delight.

As to assistance, no specific directions can he given which will meet every case. The best rule is, to afford the learner just that kind and amount, which will secure the greatest degree of exertion on his part. Less than this discourages; more, enervates.

In conclusion, we would add, that this elementary work was undertaken at the particular request of several eminent practical teachers, and is designed to fill a niche in primary schools. It presents, in a cheap form, a series of progressive exercises in the simple and compound rules, which are adapted to the capacities of beginners, and are calculated to form habits of study, awaken the attention, and strengthen the intellect.

J. B. THOMSON. NEW YORK, January, 1858.

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